Probability - Algebra - Mathematics Previous Year Questions

Let $A, B, C$ be three pairwise independent events of a random experiment. If $P(\bar{B} \cup \bar{C})=\frac{1}{2}, P(A)>0, P(B)=b$ and $P(C)=c, P((\bar{B} \cap \bar{C} \mid A)=$

Two dice are thrown and the sum of the numbers appearing on the dice is observed to be a multiple of 4 . If $p$ is the conditional probability that number 4 has appeared atleast once, then $3 p+2=$

In a random experiment of throwing 5 coins, the number of heads is defined as a random variable. The mean of the random variable is

When two dice are thrown, the probability of getting a prime number on die and a composite number on the other is

The variance of a Poisson variate $X$ is 2 . Then, $P(X \geq 3)=$

A pair of dice is thrown twice in succession. The probability of getting prime number on both the dice in first throw and composite numbers on both the dice in second throw is

If the mean and variance of a binomial distribution are 4 and $\frac{4}{3}$ respectively, then $P(X=2)=$

A cube having edge of length 5 cm is painted on all faces and then it is cut into equal cubes of unit volume. A small cube is selected at random and found that a face of it is painted, then the probability that two more faces of it are also painted is

3 balls are drawn one after the other without replacement from an urn containing 4 red, 5 blue and 6 yellow balls. The probability of getting three different coloured balls is

Two balls are drawn at random from a bag containing 5 black balls and 3 white balls. If the random variable $X$ denotes the number of white balls drawn, then the mean of $X$ is

Two bad eggs are mixed accidentally with 10 good ones. If three eggs are drawn at random from this lot in succession without replacement, then the variance of the probability distribution of the number of bad eggs drawn is

If $A$ and $B$ are two events of a random experiment such that $P(A \cup B)=P(A \cap B)$, then which one amongst the following four options is not true?

If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is

$A, B, C, D$ cut a pack of 52 well shuffled playing cards successively in the same order. If the person who cuts a spade first, wins the game and the game continues until this happens, then the probability that $A$ wins the game is

Two players $A$ and $B$ alternatively toss 3 coins simultaneously. The player who gets 2 heads and 1 tail first, wins the game. If game continues until someone wins and if $A$ begins the game, the probability that B wins the game is

In a game, two dice are thrown simultaneously by a person $A$ and two cards are drawn at random simultaneously from a pack of 52 playing cards by a person $B$. They win the game, if $A$ gets a prime score as the sum of the numbers appear on both the dice and $B$ gets a face card and a card having a prime number. Then, the probability that both $A$ and $B$ win is

A bag contains 3 red, 5 black and 7 blue balls. If three balls are drawn at random simultaneously from the bag, then the probability of getting at least two blue balls is

Three persons $A, B$ and $C$ attended a recruitment test, The ratio of the chances of $A, B, C$ in getting through the test is $1: 2: 3$ and their probabilities to face the interview successfully are $0.8,0.7,0.6$, respectively. If one of them is to be selected for the post, then the probability that $A$ gets the post is

If three unbiased dice are rolled simultaneously, then the probability that all the three dice show distinct numbers is

If two cards are drawn at random simultaneously from a pack of 52 playing cards, then the probability of getting a face card and a spade card other than the face card is